System for modular integrated optical addressing for trapped-ion quantum information processor

Abstract

Provided are an optical system for directing a plurality of light beams towards a plurality of ions at an ion trapping location, and a manufacturing method for an optical system. The optical system comprises an optics module comprising a plurality of waveguides and a deflecting element (e.g. micro mirror) which reflects light from the waveguides toward an ion trapping location. A lens system is arranged between the deflecting element and the ion trapping location to be commonly traversed by the light beams to focus each of the light beams to a respective one of the trapped ions. The present disclosure provides a scalable, modular, integrated approach for addressing ions trapped in an ion trap.

Description

[0001] System for Modular Integrated Optical Addressing for Trapped-Ion Quantum Information Processor

[0002] TECHNICAL FIELD

[0003] Embodiments of the present invention relate to the field of optical addressing for trapped ions stored in an ion trap.

[0004] BACKGROUND

[0005] Many technical applications in the field of quantum technologies (e.g. quantum computing, quantum simulations, atomic and molecular experiments, spectroscopy, atomic clocks, etc.) require the ability to precisely control the quantum states of quantum entities

[0006] For example, the quantum entity whose states are being controlled may be an ion trapped in an ion trap. A setup of such an ion trap may include a plurality of electrodes within a vacuum apparatus.

[0007] For example, in the field of quantum computing, such trapped ions are used as qubit registers. To perform quantum operations by implementing quantum gates on said ion-qubit register, the electronic and / or motional states of one or more trapped ions are being manipulated and / or entangled using laser beams directed to the trapped ions.

[0008] SUMMARY

[0009] It may be desirable to have a system for the optical addressing of ions in an ion trap that allows for flexible fabrication in accordance with the desired arrangement of the trapped ions and that is scalable with respect to the number of trapped ions.

[0010] In some embodiments, this is achieved by providing an optical addressing approach that is both integrated and allows for single-ion addressing of ion crystals with variable lengths that may exceed 5 ions.

[0011] The invention is defined by the scope of independent claims. Some of the advantageous embodiments are provided in the dependent claims.

[0012] According to an embodiment, provided is an optical system for directing a plurality of light beams towards a plurality of ions at an ion trapping location, the optical system comprising: an optics module, the optics module comprising a plurality of waveguides configured to route a plurality of light beams, and the optics module comprising a deflecting element located at an output end of the plurality of waveguides and adapted to reflect the plurality of light beams to a beam direction pointing from the deflecting element to an ion trapping location; a trap module comprising a set of electrodes, wherein the set of electrodes are arranged so as to allow for trapping of the plurality of ions at the ion trapping location; and a lens system, arranged between the deflecting element and the ion trapping location, configured to focus each of the plurality of light beams towards a respective one of the plurality of ions, the lens system comprising at least one lens arranged to be commonly traversed by all of the plurality of light beams.

[0013] These and other features and characteristics of the presently disclosed subject matter, as well as the methods of operation and functions of the related elements of structures and the combination of parts and fabrication technologies, will become more apparent upon consideration of the following description and the appended claims with reference to the accompanying drawings, all of which form a part of this specification. It is to be expressly understood, however, that the drawings are for the purpose of illustration and description only and are not intended as a definition of the limits of the disclosed subject matter.

[0014] BRIEF DESCRIPTION OF DRAWINGS

[0015] An understanding of the nature and advantages of various embodiments may be realized by reference to the following figures.

[0016] Fig. 1 is a schematic view of an optical system with a surface trap;

[0017] Fig. 2 is a cross sectional view in xy-plane of an optical system with a surface trap;

[0018] Fig. 3 is a cross sectional view in yz-plane of an optical system with a surface trap;

[0019] Fig. 4 is a detailed view in yz-plane of an optical system with a surface trap;

[0020] Fig. 5 is a cross sectional view in xy-plane of an optical system with a 3D trap;

[0021] Fig. 6 is a cross sectional view in yz-plane of an optical system with a 3D trap;

[0022] Fig. 7 is a flow chart showing steps of a method for manufacturing an optical system;

[0023] Fig. 8 shows implementations of a reflecting element a) as a reflecting surface on the groove structure and b) using total internal reflection; and Fig. 9 shows laser irradiance at the ion trapping location for an 8 channel optical addressing unit.

[0024] DETAILED DESCRIPTION

[0025] In the following description, reference is made to the accompanying figures, which form part of the disclosure, and which show, by way of illustration, specific aspects of embodiments of the invention or specific aspects in which embodiments of the present invention may be used. It is understood that embodiments of the invention may be used in other aspects and comprise structural or logical changes not depicted in the figures. The following detailed description, therefore, is not to be taken in a limiting sense, and the scope of the present invention is defined by the appended claims.

[0026] It is understood that the features of the various exemplary embodiments and / or aspects described herein may be combined with each other, unless specifically noted otherwise.

[0027] For purposes of the description hereinafter, the terms “end,” “upper,” “lower,” “right,” “left,” “vertical,” “horizontal,” “top,” “bottom,” “lateral,” “longitudinal,” and derivatives thereof shall relate to the disclosed subject matter as it is oriented in the drawing figures. However, it is to be understood that the disclosed subject matter may assume various alternative variations and step sequences, except where expressly specified to the contrary. It is also to be understood that the specific devices and processes illustrated in the attached drawings, and described in the following specification, are simply exemplary embodiments or aspects of the disclosed subject matter. Hence, specific dimensions and other physical characteristics related to the embodiments or aspects disclosed herein are not to be considered as limiting unless otherwise indicated.

[0028] No aspect, component, element, structure, act, step, function, instruction, and / or the like used herein should be construed as critical or essential unless explicitly described as such. Also, as used herein, the articles “a” and “an” are intended to include one or more items and may be used interchangeably with “one or more” and “at least one.” Furthermore, as used herein, the term “set” is intended to include one or more items (e.g., related items, unrelated items, a combination of related and unrelated items, and / or the like) and may be used interchangeably with “one or more” or “at least one.” Where only one item is intended, the term “one” or similar language is used. Also, as used herein, the terms “has,” “have,” “having,” or the like are intended to be open-ended terms. Further, the phrase “based on” is intended to mean “based at least partially on” unless explicitly stated otherwise.

[0029] Quantum computing

[0030] In quantum computing, quantum bits or qubits represent the basic unit of quantum information, corresponding to the quantum version of the binary digit (bit) representing a “0” and a “1” in a classical computer. A qubit is represented by a two-state (or two-level) quantum-mechanical system. In principal, such a quantum mechanical system may have more than two states. However, a suitable system is required to have at least two reliably distinguishable quantum states.

[0031] There are various physical systems, which include at least two distinguishable quantum states, for example, electron or nuclear spin states, atomic or nuclear states, nuclear magnetic resonance states, electronic states in quantum dots or the like.

[0032] For example, in a system using trapped ions (i.e. atoms or molecules with a net electrical charge), qubit states may be controlled and read out using radiation provided from one or more laser (light amplification by stimulated emission of radiation) beams. Suitable elements include, for example, Beryllium Be, Magnesium Mg, Calcium Ca, Strontium Sr, Barium Ba, Radium Ra, and Ytterbium Yb.

[0033] The internal qubit levels of the ion may be chosen as a ground level and a long-lived excited level, a so-called metastable level, forming a so-called optical qubit. In optical qubits, quantum information is encoded in two electronic states connected by a transition with frequency in the optical domain, i.e. a frequency in the range from 380 THz to 800 THz.

[0034] Alternatively, the qubit levels of the ion may be two different magnetic sublevels within the ground state of the ion with transition frequencies in the microwave to radiowave domain, forming a so-called Zeeman qubit or hyperfine qubit. Changing the state of a Zeeman or hyperfine qubit may involve the application of stimulated Raman transitions between the levels. Raman transitions facilitate an adiabatic transfer from a first hyperfine state to the second hyperfine state via a virtual intermediate state. Said transitions may have optical wavelengths.

[0035] Moreover, the motion of the trapped and crystallized ions becomes quantized, as the ions form a sufficiently well isolated quantum system within the ion trap. For example, the ions form a linear chain in the trap, e.g. a Paul trap, a Penning trap or the like. Ion traps are explained in detail in the section Ion traps. The motional modes, e.g. vibrational modes, of the entire linear chain of ions may be described by a quantum mechanical harmonic oscillator. Using interaction with laser beams, trapped ions may be cooled to near their motional ground state. Such cooling of the ions may involve Doppler cooling and / or resolved sideband cooling. Initialization of the internal qubits may be performed similarly by laser beam-induced transitions in individual ions. Qubits may be read out by applying a resonant laser beam to detect their fluorescence. A rapid cycling transition from one of the qubit levels to a higher excited level of the ion using such a resonant laser beam results in the emission of fluorescence photons, which may be detected, if the level is populated. If the level is not populated, no fluorescence photons will be detected.

[0036] The interaction with laser beams also facilitates transitions between the two qubit states (i.e. single-qubit operations). A pair of qubits may be entangled (i.e. two-qubit gate operations) by application of a qubit-state dependent force using laser pulses that couple the individual qubit state to the collective motional modes of the trapped ions. A similar operation may be also applied to more than two ions. These and further examples of one or more qubit operations are provided, e.g., in H. Haffner, C.F. Roos, R. Blatt, “Quantum computing with trapped ions", Physics Reports, Volume 469, Issue 4, 2008, Pages 155-203

[0037] (https: / / doi.Org / 10.1016 / j.physrep.2008.09.003) or in G. Chen, et al. Quantum Computing Devices: Principles, Designs, and Analysis. USA, CRC Press, 2019.

[0038] Ion traps

[0039] In the following, the term “ion trap” refers to any device employable to trap ions, using electric and / or magnetic field. For instance, an ion trap may be a Penning trap; a Paul trap; a three dimensional, 3D, ion trap; and / or a linear 3D trap. In this disclosure, the term ion trap refers to an assembly with a plurality of electrodes which, when driven, generate an electric field that limits (traps) the freedom of movement of ions so that they may not escape a particular (preferably small) region in the vicinity of those electrodes. It is noted that the actual ion trap device / system may include further mechanical and electrical components such as fixing means, electrical contacts, housing, power source, control circuitry, means to cool ions or the like.

[0040] An ion trap is thus a device employable to “trap” ions, i.e. employable to spatially confine ions to a particular (small) region, here also referred to as “trapping zone”. In general, ion traps use electric and / or magnetic fields to trap ions.

[0041] In such a trapping zone the trapped ions form an “ion crystal”. An ion crystal is a Coulomb crystal, comprising multiple ions that form an ordered structure in space with distinct ion positions, where the ions are spaced according to the Coulomb repulsion between the ions and the external electro-magnetic potential, e.g. from the fields used to confine the ions.

[0042] The term “Paul trap" refers to a trap that uses electric fields to trap the ions. Usually, in a Paul trap, only electric fields are used to trap the ions. In particular, usually no magnetic fields are used. In general, at least one of the electric fields of a Paul trap is alternating (e.g., oscillating), and a Paul trap may use both static as well as alternating electric fields. For example, the alternating field of a Paul trap may be an alternating electric multipole field, in particular, an electric quadrupole field. Since the switching of the voltage is often at radio frequency, these traps are also called Radio Frequency (RF) traps. The present disclosure is, however, not limited to Paul traps and also covers other types of ion traps, for example Penning traps, where a combination of electric and magnetic fields is employed to trap the ions.

[0043] Surface traps (or “surface ion traps”) are ion traps where all electrodes, generating said fields, are located (essentially) in or on a same plane. For surface traps, the trapping region is usually above the electrode plane at a distance, referred to as the ion-surface separation.

[0044] A linear surface trap is a particular type of a surface trap. Usually, in a linear surface trap, the ions are confined in two spatial directions (the so-called radial directions) using an alternating (AC) electric field and confined along the third spatial direction (the so-called axial direction or trap axis) by static (DC) electric potentials. Accordingly, a linear surface trap is in general also a (linear) Paul trap.

[0045] In the present disclosure, the term “3D trap" refers to any ion trap, which is not a surface ion trap. In a 3D trap, the electrodes are thus located on different planes. More specifically, some electrodes may be located in different planes, while some electrodes may still be in a same plane. In other words, the term 3D ion trap refers to a (three-dimensional) assembly with a plurality of electrodes which, when driven, generate electric and / or magnetic field(s) that limits the freedom of movement of ions so that they may not escape a particular (preferably small) region in the vicinity of those electrodes. For 3D traps, the trapping region is usually inside the ion trap, i.e. there are usually electrodes on different sides / directions of the trapping zone of a 3D trap. These directions may correspond to a symmetry of the 3D trap, often a continuous or discrete rotational symmetry. For instance, in case of a discrete rotational symmetry of order n, being an integer greater than 1 , there may be n electrodes at n respective directions which are related by rotations around the trap axis by angles of (360° / n) ■ m, where m = 0,1,2, ... , n - 1.

[0046] A linear 3D trap is a particular type of a 3D trap. Usually, in a linear 3D trap, the ions are confined in two spatial directions (radial directions) using an alternating (AC) electric field and confined in the third direction (axial direction) by static (DC) electric potentials. Accordingly, a linear 3D trap is in general also a (linear) Paul trap. Henceforth, without loss of generality, the axial direction of a surface linear trap or a 3D linear trap is assumed to be parallel to the z-axis of a Cartesian coordinate system in which the axes are represented by three mutually orthogonal unit vectors ex, ey, and ez. For a surface trap, the axial direction often corresponds to a translational symmetry of the electrode geometry. A 3D trap often has cylindrical symmetry around the trap axis. The direction r(x,y) = (xex+ yey) / %2+ y2is referred to as the “radial direction” (at the point (x,y, 0) = xex+ yey). It is further noted that the trap axis may also be the axis along which multiple trapped ions typically align, i.e. the axis of a chain of trapped crystallized ions is typically identical with the trap axis.

[0047] Embodiments

[0048] In a trapped-ion processor, trapped ions forming linear crystals are used as qubits. The ionqubits in a crystal form a (sub-) register of qubits. Quantum gate operations on ion-qubits are realized using laser radiation.

[0049] Single-qubit gates require laser light to be focused onto a single ion, while other ions in the ion crystal should experience negligible cross talk. Accordingly, other ions should not be exposed to laser intensity of the addressing beam. Likewise, two-qubit systems require only a subset of ions in the crystal to be addressed with laser light, while all other ions in the crystal should experience negligible cross talk.

[0050] Exemplary approaches to single-ion addressing include non-integrated systems, e.g. free- space optics where a laser beam is directed toward the vacuum environment from the outside. Other, integrated, approaches are limited to short ion crystals with not more than approximately 5 ions due to the large footprint of the employed integrated optical elements.

[0051] The present disclosure provides an approach to optical addressing which is both integrated and facilitates single-ion addressing of ion crystals with greater lengths exceeding 5 ions.

[0052] Provided is an optical system for directing a plurality of light beams toward a plurality of ions at an ion trapping location.

[0053] As shown in Fig. 1 , the optical system comprises an optics module 110, a trap module 120 and a lens system 130.

[0054] The optics module 110, which may be referred to as an “optics chip”, comprises a plurality of waveguides 111 configured to route a plurality of light beams. The waveguides may thereby be arranged at a surface or close to a surface of the optics module facing the trap module 120. The optics module further comprises a deflecting element 112 located at an output end of the plurality of waveguides 111 and adapted to reflect the plurality of light beams to a beam direction pointing from the deflecting element 112 to an ion trapping location 121.

[0055] The deflecting element 112 may be a single element that deflects all beams of the plurality of light beams, or the deflecting element may be a set of deflecting elements, e.g. one for each waveguide of the plurality of waveguides 111 , or a combination thereof.

[0056] The trap module 120, which may be referred to as a “trap chip”, comprises a set of electrodes 125. The set of electrodes are arranged so as to allow for trapping of the plurality of ions at the ion trapping location 121.

[0057] The trap module may furthermore comprise an optically traversable portion providing optical access for the plurality of light beams from the deflecting element towards the ion trapping location. The optically traversable portion may accommodate the lens system 130. As will be described further, the optically traversable portion may for instance be an opening slot in the chip substrate and trap electrodes. However, also other means of optical access such as an optically transparent window created by a transparent substrate and / or transparent conducting trap electrodes may be used.

[0058] The lens system 130 (or “focusing lens system”), which may be referred to as “micro optics”, is arranged between the deflecting element 112 and the ion trapping location 121. The lens system 130 is configured to focus each of the plurality of light beams towards a respective one of the plurality of ions. The lens system 130 comprises at least one lens, and the at least one lens is to be commonly traversed by the plurality of light beams. In other words, all of the plurality of light beams traverse a same lens or same lenses of the lens system 130.

[0059] Each of the plurality of light beams is directed towards one of the plurality of ions. Accordingly, a one-to-one correspondence between the light beams as addressing beams and the respective ions may be provided.

[0060] The plurality of ions may form an ion chain or ion string along a direction parallel to a direction along which the deflecting element 112 is arranged at the output end of the waveguides.

[0061] The optics module 110, or optics chip, may comprise a photonic integrated circuit (PIC). A photonic integrated circuit is a chip that contains photonic components, which are components that modify the propagation of light (photons), e.g. by confining and guiding the light, by switching the light propagation between different optical channels, by modifying the light phase or frequency, or the like. The plurality of waveguides may be part of the PIC and may be used to route or guide the plurality of light beams (e.g. laser light) on the optics module 110 before deflection by the deflecting element 112. The light may be routed by the plurality of waveguides, which may form separate optical channels, e.g. mutually independent and isolated optical channels. Each of the plurality of waveguides may route a respective one of the plurality of light beams. Thus, since each light beam, after deflection, focuses a respective one of the plurality of ions in a one-to-one correspondence between light beams and ions, it is possible to provide desired light parameters, e.g. including laser light intensity, laser light frequency, from an input channel individually for each trapped ion. The output end of the plurality of waveguides may be formed as a free-space outcoupling element. As an example, SisN4 waveguides may be used as the plurality of waveguides for optical routing.

[0062] It is noted that additional optical components, which will be described further (e.g. polarizers, voltage-controlled attenuators, switches, combiners or multiplexers), may be part of these routing lines to manipulate the laser light.

[0063] Moreover, the optics module 110 and / or micro optics 130 may comprise coatings of the optical elements. For instance, the coating may include anti-reflection coating for the waveguide outcoupling or the deflecting element, and / or a conductive transparent coating (e.g. indium- tin-oxide coating) for the micro optics (i.e. the lens system) 130 on the side facing the ions such as to further reduce the impact of electric stray fields and electric field noise.

[0064] Light, e.g. laser light, in the individual waveguides may be supplied through individually controllable optical supply channels or input channels, such that the laser light intensity, laser frequency and / or other parameters at any given ion location can be switched at will. One or more control units, which control the light beams and their light parameters, may be comprised by the optics chip or provided as an external control unit or control units. For instance, the waveguides may be fiber-coupled to external control units, or may be connected to an integrated optical control unit.

[0065] Alternatively, or in addition to the separate optical channels, a multiplexer may be used for multiplexing an optical input channel with given parameters to a plurality of light beams directed to a plurality of ions forming (sub-) registers, or multiplexing M (e.g. M=2, 3, ...) input channels to N (with typically N > M) output channels directed to N ions.

[0066] The light of the plurality of light beams may be coupled out of the waveguides through a groove in the PIC chip, such that the waveguides end on a plane facet and the light is transmitted into the groove, e.g. into free space. Alternatively, the groove at the output end of the waveguides may also be filled with an optical transparent material. Alternatively, or in addition, the plurality of waveguides may have waveguide tapers at their output end, up to the point where the waveguides completely vanish, and the light propagates in the cladding or transitions to a different guiding material which may be part of the deflecting element 112, e.g. made from 3D- printed polymers.

[0067] As can be seen in Figures 1 and 2, the plurality of waveguides 111 may be guided in a plane substantially parallel to a surface of the optics chip where the trap chip is mounted to the optics chip.

[0068] The spacing of the waveguide end facets at the output end of the PIC determines the spacing of the light beams at the positions of the trapped ions at the ion trapping location, with a possible magnification factor given by the lens system 130. The spacing of the waveguide end facets can be chosen by design of the waveguide structures in accordance with a desired spacing of ions at the ion trapping location 121. For instance, one may choose an unequal spacing of the waveguide end facets to exactly match the unequal spacing of ions in an ion chain confined in a harmonic potential, where ions towards the end of the chain have a larger spacing compared to ions at the chain center.

[0069] It is noted that in Figures 1 to 6, the x, y and z axis are axes of a Cartesian coordinate system where the surfaces of the optics module 110 are parallel to the xz plane, with the waveguides 111 being guided along a direction parallel to the x axis. The light path from the deflecting element 112 to the ion trapping location 121 follows the y axis.

[0070] The deflecting element 112 at the output end of the waveguides is an optical element used to change the propagation-direction of the out-coupled laser beams exiting the waveguides from being in-plane with the optics chip surface to being near perpendicular to it. In other words, the beam direction after deflection at the deflecting element 112 may be substantially perpendicular to a waveguide direction along which the plurality of waveguides are directed to guide the light beams.

[0071] The deflecting element 112 may deflect the plurality of beams by reflection. For example, the deflecting element may comprise a mirror or micro-mirror such as a metalized mirror, a dielectric mirror, a refractive mirror or an optical element using total internal reflection, a plurality of any one of the listed elements, or a combination of different elements from among the listed elements. For instance, as mentioned above, the deflecting element may comprise, a single mirror (or other element) for all waveguides, a respective mirror / element for each waveguide, or a first mirror / element for a fist subset of waveguides, a second mirror / element for a second set of waveguides, etc. The deflective element may be realized on the groove structure itself, e.g. carved into the optics chip in an angle that defines the angle at which the light beams are deflected, and be provided with a reflecting surface, e.g. metalized. This is illustrated in Fig. 8 a). The deflecting element may also be realized without the groove structure, for instance using an angled slot in the waveguides (illustrated as core and cladding in Fig. 8) creating total internal reflection of the light beams at the angled facet, as illustrated in Fig. 8 b). It is noted that the laser beam envelopes shown in Fig. 8 are merely schematic and not to be understood as limiting with respect to the size or shape of the laser beam envelopes for the different implementations shown in parts a) and b). In particular, the laser beam envelopes do not necessarily need to differ with regard to the laser beam envelopes. Alternatively, the deflecting element may be realized using a 3D printed optical element with a total internal reflection facet to which the guided light mode is adiabatically transferred using a suitable waveguide taper.

[0072] Alternatively, an active deflection element such as an acousto-optic or electro-optic modulator may be used as a deflecting element.

[0073] The trap module 120 may comprise a trap module body and a set of electrodes 125. The electrodes may be arranged on the trap module body, e.g. at one side of the trap module. For instance, the trap module body is formed at least partially from an insulating material, e.g. an insulating substrate, or from metal. For instance, e.g. in embodiments with a 3D trap to be described later, electrodes may be massive metal parts or may be formed by a conductive (e.g. metal) coating on a dielectric body. In the case of massive metal electrodes, the electrodes may be held in a mount, e.g. a cage-like support, made at least partially of an electrically insulating material, which may be a ceramic, a glass, or a crystalline material such as sapphire.

[0074] It is noted that the term “ion trapping location” refers to a region where ions are trapped and is not limited to any shape or number of dimensions and may refer to any arbitrary region or arrangement where a plurality of ions are trapped. The ion trapping location may also be referred to as “ion trapping region” or “ion trapping zone”. Since there are a plurality of trapped ions, the ion trapping location 121 has an extension in at least one dimension where the trapped ions are arranged at a plurality of ion positions along that dimension, e.g. a straight line. However, an ion trapping location may be an arbitrary arrangement of a plurality of ions, e.g. a line, two (or more) lines (or “linear zones”) in two-dimensional space, which may be parallel or connected by junctions, a triangular shape, or a (rectangular, hexagonal etc.) lattice. As a further possibility, a two-dimensional ion crystal may be stored in a quantum well. Further, the present disclosure is not limited to a single trapping location. It may also be, that a plurality of ions is distributed over two or more mutually different (e.g. spatially separated) ion trapping locations, which are in close proximity such that a plurality of light beams from the optics module can interact with these trapped ions. For instance, two linear parallel trapping zones may be addressed by a single arrangement of an optics module and a lens system. The optics module and the lens system may then be arranged at a central location along an axis in the horizontal plane (xz plane in Fig. 1) between the linear trapping zones.

[0075] The trap module, or trap chip, is stacked on top of the optics module, e.g. a chip surface trap stacked on top of the optics chip, with ions being trapped above the trap electrodes at the ion trapping location on the trap chip’s far side of the optics chip. It is noted that the substrate of the trap chip 120 may be made of a material different from the material of the optics chip 110.

[0076] As described above, the trap module 120 may comprise an optically traversable portion, which may accommodate the lens system 130. The trap module 120 may have a slot 122 accommodating or enclosing the lens system.

[0077] The slot in the trap module may be arranged in a manner so as to allow the light beams to be directed within the slot after deflection at the deflecting element 112 and pass through the lens system within the slot before leaving the slot through a slot opening and hitting the trapped ions at the ion trapping location. The slot 122 may be arranged beneath the ion trapping location as an addressing slot, creating free-space optical access for the deflected light beams to the ions, e.g. going through the entire trap chip substrate.

[0078] For instance, as shown in Figures 2 to 4, the slot is formed as a cavity within the trap module body to provide as optical access for the light beams to the ion trapping locations, e.g. in a substrate provided between the optics module 110 and the electrodes. Alternatively, as shown in Fig. 5, the slot may be formed by the shape of the electrodes. While Fig. 5 shows dielectric electrodes with conductive coating, the electrodes may also be massive metal, as mentioned above. In the latter case the electrode mount would need to have a suitable opening as well.

[0079] The slot 122 may have electrically conducting side walls. For instance, the side walls of the slot may be metallized or coated with a material such as Indium-Tin-Oxide or a semiconductor material having sufficient electrical conductivity.

[0080] A distance between the lens system and an opening of the slot facing the trapping location may be larger than a width of the opening of the slot. In other words, the opening or “aperture” of the slot may form a gap between opposite edges of the slot, which is smaller than a distance between the slot opening and the lens system. It is noted that the length of the slot is not limited by the distance between the slot opening and the lens system. Rather, the length of the slot may be chosen to be sufficient for all light beams to reach the respectively corresponding ion. With a slot as described herein, the lens system is hidden from the trapped ions, as the lens system is located in the slot of the trap chip, where the slot may have metallized side walls, which may be electrically grounded, such as to reduce the impact of electric stray fields and electric field noise emanating from the lens system and / or from the optics module. For instance, the distance between lens system and the trap surface may be larger than the width of the rectangular (or otherwise shaped) aperture defining the slot at the trap surface.

[0081] In other words, having a slot and a slot opening may provide for a suitable shielding of the ions at the ion location 121 from undesired stray charges and / or other electric field noise. The shielding may be further enhanced by the slot having electrically conducting side walls.

[0082] As an example, in Figures 2 and 3, a narrower slot width (along x axis direction) of 60 pm, and a wider slot length (along z axis direction) of 250 pm is shown. However, the present disclosure is limited neither to particular values of the width of the slot opening along different directions nor to a particular shape of the slot opening. The length of the slot may stretch over the entire length of the trap chip, or may be as small as a size comparable to the ion crystal, e.g. from 5mm to 5pm. The width of the slot may be as small as the width of the laser beam. For instance, the minimum width of the slot may be 2 times the wavelength of the laser light, e.g. a slot width of around 1 pm to 2pm. The maximum width of the slot may be defined by the ability of the slot to create notable shielding of stray charges and noise from the micro optics. To provide for such shielding, the slot width should at most be the distance of the micro optics to the slot opening facing the trapped ions, with the ultimate limit being the trap chip thickness. In Fig. 2 this would be 500pm as a limit of the slot opening. Further, when considering the maximum limit, the width of the slot should be chosen in such a manner that the functionality of the ion trap is not impaired. The slot opening may be rectangular but may also deviate therefrom, for instance at the corners, or be an entirely different shape.

[0083] Further, in Fig. 2, a distance between the slot opening and the ion location 121 is exemplarily shown as 100 pm and thus larger than the slot width of 60 pm. However, this example is not limiting as a suitable ratio between a width of the slot opening and a distance between the slot opening and the ion trapping location may be selected in accordance with the accuracy of alignment of the light beams or trapped ions or with the magnification provided by the lens system on the one hand, and the shielding performance of the slot and aperture on the other hand.

[0084] Furthermore, as shown in Figures 2 and 3, the slot width may taper, or shrink in a stepwise fashion, from an opening facing the optics module to the above-described opening facing the ion trapping location. Thus, the required space for the micro-optics 130 may be achieved without impact on the trap electrode geometry or the shielding performance given by the slot opening facing the ion trapping location.

[0085] The lens system 130, also referred to as “micro optics”, comprises at least one lens through which the light beams are propagating, which may be a micro-manufactured optical lens (which may be referred to as “microlens”) or a plurality of micro-manufactured lenses. Possible types of microlenses include, for instance, aspherical lens, meniscus lens, Fresnel lens, achromatic lens, or cylindrical lens. For instance, the lens system may be a stack of micro-lenses comprising one or more lenses such as the aforementioned types of lenses. For instances, microlenses may be used where the focusing of the light beams is based on refraction, and where geometrical optics is applicable. In some embodiments, the lens or lenses of the lens system do not include meta-lenses where the focusing is based on diffraction rather than refraction.

[0086] The lens system 130, which is placed between the deflecting optical element 112 and the trapped ions, is used to focus the divergent laser beams onto the ions at the ion trapping location 121. Accordingly, the lens system forms an optical image of the waveguide end facets on the trapped ions with a given magnification factor, which can be chosen by design of the lens system.

[0087] In addition to defining the magnification factor of the image of waveguide ends at the ion trapping location, the lens system 130 may allow for providing a well-defined and sufficiently precise intensity profile or shape of the beams. For instance, one or more lenses of the lens system 130 may be a cylindrical lens with different focal lengths along two different directions. In addition or instead, the waveguides 111 may be designed such as to emit an elliptical beam shape, for instance by a suitable waveguide taper towards the outcoupling region. The waveguide design together with the lens system 130 may thus allow adjustment of the ellipticity of the laser beam radial intensity profile at the ion trapping location 121. In Fig. 2, an exemplary beam diameter in x-direction of the laser beams of the plurality of light beams at the ion trapping location is shown as 20 pm. In Fig. 4, an exemplary beam half diameter in the z- direction of the laser beams of the plurality of light beams is shown to be substantially smaller than the ion-ion spacing of approximately 3-4 pm, for instance 1-2 pm, to suppress optical cross talk.

[0088] Figs. 3 and 4 illustrate how the plurality of laser beams traverse through a common lens 130 such that the waveguide output is imaged onto the trapped ions, providing a one-to-one correspondence between the light beams as addressing beams and the respective ions. For instance, as shown in Fig. 4, the addressing beam 1 from waveguide 111-1 is focused onto ion 1 , with negligible light intensity (cross talk) on the neighboring ion 2. Likewise, the addressing beam 2 from waveguide 111-2 is focused onto ion 2, with negligible light intensity (cross talk) on the neighboring ion 1. As mentioned, a combination of the magnification factor and the spacing of waveguide ends can be chosen to match the spacing of ions at the ion trapping location. For instance, a distance between two neighboring ion positions at the ion trapping position is a magnification factor times the distance between two neighboring waveguide ends of the plurality of waveguides, wherein the magnification factor is between 0.1 and 10. An exemplary magnification factor is 1 (the distance between neighboring waveguides being substantially the same as the distance between neighboring ion positions), which ensures scalability to large numbers of ions in the ion chain as the waveguides’ footprint in the outcoupling region exactly matches the ion chain length. For instance, as shown in Fig. 4, the distance between two adjacent ions in the ion chain, ion 1 and ion 2, may be 4 pm. At a magnification factor 1 of the lens system 130, the spacing between the corresponding waveguides 111-1 and 111-2 will thus also be 4 pm.

[0089] It is noted that the above-mentioned bounds of the range for the magnification factor are provided for the following reasons. The larger the magnification is, the more closely spaced the waveguides need to be. For instance, at an ion-ion spacing of 4pm and magnification M=10, the beam spacing at the location of the deflecting element is 400nm. Further reducing the waveguide spacing may result in more cross talk, and / or optical loss in the waveguides, or they may impede the manufacturing of the waveguides. For M=0.1 , at an ion-ion spacing of 4pm, the beam spacing at the location of the deflecting element would be 40pm. For instance, for an ion chain with 10 ions, the waveguides would span approximately 400pm. Further increasing the waveguide spacing may cause footprint issues since the waveguides need more space and also the common lens in lens system 130 would need to be larger. It is noted that the bounds are to be considered “soft” bounds, which may be varied depending on how many ions one wants to address.

[0090] It is further noted that different optical channels may have different wavelengths of the light. For instance, in addition to the optical channels for addressing the trapped ions, optical channels at different wavelengths may be added for additional functionality, e.g. laser cooling, imaging, repumping, etc. To focus beams at different wavelengths, the lens system may include one or more achromatic lenses at two, three or more wavelengths. In such a polychromatic application some of the optical channels may be routed not parallel to the waveguides 111 shown in Figs. 1 and 2, but be routed at an angle, or be parallel to the waveguides 111 but be routed from the opposite end (i.e. from the -x direction in Figs. 1 and 2). Consequently, the output deflection elements of these optical channels may be somewhat off the optical axis of the lens system 130, in the xz-plane. In the following, additional optical components are described that may be part of the routing lines of the plurality of light beams to manipulate the laser light, which may be provided either in the optics module 110 or in an additional PIC module attached to the optics module.

[0091] For instance, the photonic integrated circuit may further comprise one or more elements for controlling one or a combination of a light frequency or phase, or a light amplitude, or a light polarization of each of a plurality of separate optical supply channels, which supply the waveguides 111 with the light at an input end. Such elements may comprise one or more control units or control circuitry. Exemplary elements for controlling a light frequency or phase include an electro-optic modulator or acousto-optical modulator. The light amplitude may be controlled, for instance, by use of an acousto-optical modulator, by an integrated interferometer, or by adjusting or modifying the power supply of the light source, e.g. the laser.

[0092] Here, each of the plurality of optical supply channels may corresponds to a respective one of the plurality of light beams. In such a case, each frequency and / or amplitude light beam of each light beam may be controlled individually.

[0093] However, the present disclosure is not limited to a one-to-one correspondence between optical supply channels and light beams. Alternatively, the optics module 110 may further comprise an optical multiplexer configured to multiplex a first number of the optical supply channels to a second number of optical output channels corresponding to the plurality of light beams.

[0094] It is noted that combination of one-to-one correspondence and multiplexing is also possible, where one or more of the light beams correspond to respective supply channels, and other light beams among the plurality of light beams are multiplexed.

[0095] Furthermore, as mentioned above, there may be a plurality of deflecting elements rather than a single deflecting element 112. For instance, for two or more optical channels, each of which may or may not be multiplexed into a plurality of light beams, there may be two or more corresponding independent deflecting elements, e.g. micro mirrors each corresponding to an optical channel. The micro mirrors may be tunable, e.g. electrically adjustable, such that their output beam angle may be tuned to address different ions in the string.

[0096] As mentioned above, the light source(s) of the plurality of light beams, e.g. a laser light source or sources, may be arranged outside the vacuum environment, whereas the components of the optics chip 110, as well as the trap chip 120 and the lens system 130 described herein are placed within the vacuum environment of vacuum chamber. Fiber coupling, for instance edge coupling or grating coupling, may be provided to connect the laser source(s) to the optics chip 110 and the plurality of waveguides 111 and to couple the light from the light source(s) into the waveguides.

[0097] Light from the waveguides may have a certain polarization state, e.g. linear polarized light, and also a certain optical mode, for instance a TEMoo mode, TEM01, or other TEM (transverse electromagnetic), TE (transverse electric) or TM (transverse magnetic) modes. The polarization state and optical mode may be maintained by the subsequent lens system 130.

[0098] However, in some embodiments, the lens system 130 and / or the optics chip 110 may comprise one or more elements for controlling one or a combination of: light polarization, optical mode (e.g. TEMoo, TEM01, etc.), mode shape (e.g. the ellipticity of the TEMoo mode) or beam angular momentum of the plurality of light beams.

[0099] It is noted that while the at least one focusing lens of the lens system 130 is commonly traversed by a plurality of light beams, other optical elements, including those for controlling the above-mentioned light properties, may be provided to be traversed by or otherwise control the light of all light beams, a subset of the light beams, or individual light beams.

[0100] Exemplary elements for controlling light polarization, optical mode or mode shape and / or beam angular momentum include a polarization filter, a waveplate, a phase plate, a spatial light modulator, or an optical mode converter. For instance, a waveplate or waveplates may be provided in the optics module 110 and / or in the lens system 130 for controlling the polarization of the light beams. A phase plate or phase plates may be provided in the lens system 130 (i.e. the micro optics) for controlling the optical mode of the light beams, e.g. to generate from a Gaussian TEMoo mode transversal electric modes (TEM) of higher radial and / or angular mode order and or light beams with an orbital angular momentum (vortex beams).. For the same purpose, an integrated optical mode converter in the optics chip may be used Cylindrical lenses in the micro optics 130 or waveguides with adjusted (tapered) cross section in the optics chip 110 may be provided to control the mode shape, e.g. the ellipticity of the mode profile, of the laser beams, as already described in the previous paragraphs.

[0101] As shown in Figures 1 to 3, the set of trap electrodes may be arranged on a surface of the trap module 120 on the far side of the optics module 110 (i.e. a surface facing away from the optics module) and form a surface trap. The trap module may hold the ions at an ion trapping location at a distance from the surface on the opposite side of the surface electrodes with respect to the substrate and the optics module 110.

[0102] It can be seen in Figures 2 and 3 that the slot 122 is embedded or recessed within the substrate of the trap module 120. It is further noted that the width of the trap chip along the (y axis) direction of the light path between the deflecting element and the electrodes (the substrate “thickness”) is merely exemplarily shown as 500 pm. For instance, the width along y axis direction may be within a range from 50 to 5000 pm.

[0103] Alternatively, as shown in Fig. 5, the set of electrodes of the trap module may be arranged in a three-dimensional pattern around the ion trapping location and form a three-dimensional trap (3D trap).

[0104] In a 3D trap, the electrodes may for instance be formed by a metallic coating on an insulating substrate, as shown in Fig. 5, or the electrodes may be massive metal electrodes held in an insulating mount. For instance, as shown in Fig. 5, two electrodes 525-1 may be attached to a surface of the optics chip 110 (the surface where the deflecting element 112 is arranged), and two further trap electrodes 525-2 may be arranged on an opposite side of the ion trapping location in such a manner that the four trap electrodes form a symmetrical pattern with two or four axes of reflection symmetry around the ion trapping location.

[0105] In embodiments with a 3D trap, a slot 522, which accommodates the lens system 130, may be provided as a gap between the two electrodes 525-1 of the trap module adjacent to the optics chip 110. An exemplary slot width is shown in Fig. 5 as 80 pm, and a distance between ends of the electrodes and a center of the ion trapping location is shown as 150 pm. Due to the gap between respective pairs of electrodes, the electrodes are not shown in the cross section in the yz plane shown in Fig. 6.

[0106] As in the example shown in Figures 1 to 6, the lens system 130 may be arranged at half distance between the deflecting element 112 and the ion trapping location 121 (here, an exemplary distance between the lens system and the ion trapping location is 300 pm within a light path between the deflecting element and the ion trapping location of length 600 pm), but the lens system may be arranged at a different position within the light path, e.g. closer to or further away from the optics module 110.

[0107] In addition to the optical system described above, the present disclosure provides a method for manufacturing an optical system for directing a plurality of light beams towards a plurality of ions trapped by an ion trap. As shown in Fig. 7, the method comprises step S71 O of providing an optics module. The optics module comprises a plurality of waveguides. The method further comprises step S720 of incorporating, into the optics module at an output end of the plurality of waveguides, a deflecting element. Further, the method comprises step S730 of providing a trap module. The trap module comprises a set of electrodes, which are arranged so as to allow for trapping of the plurality of ions at an ion trapping location. The method further comprises step S740 of arranging a lens system between the deflecting element and the trapping location. In addition, the method comprises step S750 of attaching the trap module to the optics module.

[0108] In step S710, the optics module with the waveguides, that may have a free-space outcoupling element at the waveguide ends, may be manufactured using PIC processes. For instance, the waveguides may be lithographically fabricated Silicon Nitride (SisN^ , Aluminum Nitride (AIN) or Aluminum Oxide (AI2O3) waveguides on a Si or glass substrate, or laser-written-waveguides in glass.

[0109] Step S720 of incorporating the deflecting element includes etching or depositing a profile at a given angle on a surface of the optics module.

[0110] For instance, the deflecting element, e.g. a micro-mirror, may be monolithically integrated with an optics chip such as a PIC chip forming the optics module. Exemplary techniques for incorporating the deflecting element include etching a 45° profile out of the chip at the location of the waveguide facets using grayscale lithography, and subsequently metallizing the 45° profile. Exemplary techniques for depositing the deflecting element in an additive manner include depositing or applying a 45° ramp on the optics chip and subsequently metallizing the ramp. For instance, the ramp may be deposited using 3D printing. Deflecting elements can be also fabricated by total-internal-reflection elements within every waveguide by focused-ion beam milling.

[0111] In step S730, the ion trap, in particular in embodiments with a surface trap where the ion trap module comprises a substrate with a through substrate slot, may for instance be realized from a glass substrate using a selective laser etching (SLE) process, with subsequent metallization of trap electrode surfaces. Alternatively, a deep-reactive ion etching process on a Silicon substrate may be used to form the slot, with electrodes realized by lithographic processes.

[0112] Step S740 of arranging the lens system may include forming the at least one lens by three- dimensional printing of one or more lenses (e.g. polymer lenses) on the optics module, by selective laser etching of the one or more lenses out of a substrate material, e.g. a glass substrate, by inserting the lens system in a slot of the trap module, or by providing the lens system on a separate substrate, e.g. a separate glass substrate.

[0113] Here, “separate” means a separate substrate from the substrate of the trap module, in case the trap module has a substrate. In case the trap module has massive electrodes, the lens system may be inserted between the massive metal electrodes or their mounts.

[0114] The lens system may be realized using 3D printed polymer optics (e.g. printed onto the optics module and thereby attached to the optics module). Alternatively, the lens system can be monolithically realized as part of the trap chip or trap module using e.g. an SLE or nanoimprint process.

[0115] Step 750 of attaching the trap module to the optics module may be performed by mounting the trap module to the optics module so as to form an optical path for a light beam leading (or pointing) from the deflecting element to the ion trapping location.

[0116] Attaching step S750 may performed by a wafer bonding process, or by using a glue, or by using a mechanical fixture.

[0117] For instance, a connection between the trap and optics chips, to form a single piece, can be made using a chip bonding technique, e.g. plasma-activated fusion bonding, thermocompression bond, or using an UHV-compatible epoxy glue. As a mechanical fixture, tongue and groove may be provided.

[0118] With an optical system and a manufacturing method as described, the present disclosure provides a scalable approach to optical addressing of trapped ions stored in an ion trap.

[0119] In particular, the approach of the present disclosure is modular in that optics components including waveguides are forming one element (“optics module”), while the ion trap is forming a second element (“trap module”). The modules can be independently manufactured, and later brought together to form a single unit.

[0120] Furthermore, the approach of the present disclosure is integrated as the addressing optics are realized with integrated micro-fabricated structures, comprising: a number of independent optical channels for routing the laser light on the “optics module”, and a subsequent optical element (OE corresponding to the above-described lens system) focusing all of the individual laser beams onto the ion plane. In particular, the OE is a lens or a system or stack of lenses, which may include a Fresnel lens. The OE or lens system may be realized as part of the “optics module” or as part of the “trap module”, or as a separate element. Once the optics module and the trap module have been connected together forming a single unit, the addressing approach of the present disclosure does not require any additional alignment procedure to overlap the laser beams with the ions, in particular in embodiments where the micro mirrors are passive devices.

[0121] Moreover, with the combination of waveguides with a micro mirror as a deflecting element and a micro lens as a lens system, the disclosed optical system facilitates obtaining precise and stable polarization states of the laser light, which are an important factor in maintaining stable quantum gates as the light polarization has an effect on the coupling strength between the laser light and the trapped ions. With the combination of the waveguides, micro mirror and micro lens as disclosed, the polarization state of the light, as set by control elements in the optics chip, can be maintained.

[0122] Furthermore, the provision of a micro mirror and a micro lens facilitates collimation of the laser beams in the region of the lens system. As a result, polarization state can be modified or adjusted by waveplates or other optical elements that may be provided in addition to the one or more lenses of the lens system.

[0123] The addressing approach of the present disclosure is scalable as the number of optical channels can be scaled up with the number of ions in the ion chain without impeding the functionality or performance of the device. In particular, the use of a common lens, e.g. a microlens, for the plurality of light beams, as well as the integrated modular design, facilitate the provision of an optical system where each ion in the ion chain can be addressed with sufficient accuracy. Furthermore, the approach is suited for single-ion addressing of ions in a linear ion crystal: the optics module provides multiple laser beams which are tightly focused to deliver laser light to a single ion within the crystal each, with negligible light intensity on all other ions in the crystal.

[0124] As an example, simulated laser irradiance at the ion trapping location is shown for an eight channel optical addressing unit in Fig. 9 from a simulation of an optical system in accordance with the present disclosure.

[0125] Possible areas of applicability of the present disclosure include ion traps, quantum information processing, as well as metrology and sensing applications.

[0126] Summarizing, provided are an optical system for directing a plurality of light beams towards a plurality of ions at an ion trapping location, and a manufacturing method for an optical system. The optical system comprises an optics module comprising a plurality of waveguides and a deflecting element (e.g. micro mirror) which reflects light from the waveguides toward an ion trapping location. A lens system is arranged between the deflecting element and the ion trapping location to be commonly traversed by the light beams to focus each of the light beams to a respective one of the trapped ions. The present disclosure provides a scalable, modular, integrated approach for addressing ions trapped in an ion trap.

Claims

CLAIMS1 . An optical system for directing a plurality of light beams towards a plurality of ions at an ion trapping location, the optical system comprising: an optics module, the optics module comprising• a plurality of waveguides configured to route a plurality of light beams, and• a deflecting element located at an output end of the plurality of waveguides and adapted to reflect the plurality of light beams to a beam direction pointing from the deflecting element to an ion trapping location; a trap module comprising a set of electrodes, wherein the set of electrodes are arranged so as to allow for trapping of the plurality of ions at the ion trapping location; and a lens system, arranged between the deflecting element and the ion trapping location, configured to focus each of the plurality of light beams towards a respective one of the plurality of ions, the lens system comprising at least one lens arranged to be commonly traversed by all of the plurality of light beams.

2. The optical system according to claim 1 , wherein the trap module has a slot enclosing the lens system.

3. The optical system according to claim 2, wherein the slot has electrically conducting side walls.

4. The optical system according to claim 2 or 3, wherein a distance between the lens system and an opening of the slot facing the ion trapping location is larger than a width of the opening of the slot.

5. The optical system according to any one of claims 1 to 4, wherein the at least one lens includes a micro-manufactured optical lens.

226. The optical system according to any one of claims 1 to 5, wherein the deflecting element comprises: one or more metalized mirrors, one or more dielectric mirrors, refractive mirrors, or one or more optical elements using total internal reflection.

7. The optical system according to any one of claims 1 to 6, wherein said beam direction after deflection at the deflecting element is substantially perpendicular to a waveguide direction along which the plurality of waveguides are directed to guide the light beams.

8. The optical system according to any one of claims 1 to 7, wherein the optics module comprises a photonic integrated circuit of which the plurality of waveguides are part of, wherein the photonic integrated circuit comprises one or more elements for controlling one or a combination of a light frequency or phase, or a light amplitude, or a light polarization of each of a plurality of separate optical supply channels, wherein each of the plurality of optical supply channels corresponds to one of the plurality of light beams or the optics module further comprises an optical multiplexer configured to multiplex a first number of the optical supply channels to a second number of optical output channels corresponding to the plurality of light beams.

9. The optical system according to any one of claims 1 to 8, wherein one or both of the optics module or the lens system comprises one or more elements for controlling one or a combination of: light polarization, optical mode, mode shape, or beam angular momentum of the plurality of light beams.

10. The optical system according to any one of claims 1 to 9, wherein a distance between two neighboring ion positions at the ion trapping location is a magnification factor times a distance between two neighboring waveguide ends of the plurality of waveguides, and the magnification factor is between 0.1 and 10.11 . The optical system according to any ones of claims 1 to 10, wherein the set of electrodes are arranged on a surface of the trap module on a far side of the optics module to form a surface trap, or wherein the set of electrodes are arranged in a three-dimensional pattern around the ion trapping location to form a 3D trap.

12. A method for manufacturing an optical system for directing a plurality of light beams towards a plurality of ions trapped by an ion trap, the method comprising the steps of: providing an optics module, the optics module comprising a plurality of waveguides; incorporating, into the optics module at an output end of the plurality of waveguides, a deflecting element; providing a trap module, the trap module with a slot comprising a set of electrodes, wherein the set of electrodes are arranged so as to allow for trapping of the plurality of ions at an ion trapping location;. arranging a lens system including at least one lens between the deflecting element and the trapping location; and attaching the trap module to the optics module.

13. The method according to claim 12, wherein the step of attaching is performed by a wafer bonding process, or by using a glue or by using a mechanical fixture.

14. The method according to claim 12 or 13, wherein the step of incorporating the deflecting element includes etching or depositing a profile at a given angle on a surface of the optics module.

15. The method according to any one of claims 12 to 14, wherein the step of arranging the lens system includes forming the at least one lens by three-dimensional printing of the at least one lens on the optics module, by selective laser etching of the at least onelens out of a substrate material, by inserting the lens system in a slot of the trap module, or by providing the lens system on a separate substrate.

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